A General Framework for Endowment Effects in Combinatorial Markets
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The endowment effect, coined by Nobel Laureate Richard Thaler, posits that people tend to inflate the value of items they own. We study endowment equilibria --- Walrasian equilibria in combinatorial markets with valuations that are subject to the endowment effect. While standard Walrasian equilibria are guaranteed to exist only for the restricted class of gross substitutes valuations, a recent work of Babaioff et al. [EC'18] showed that for a particular formulation of the endowment effect, every market with submodular valuations admits an endowment equilibrium. Moreover, this equilibrium gives at least half of the optimal social welfare. Unfortunately, their existence guarantee provably fails to extend to the broader class of XOS valuations. We devise a general framework capturing a class of endowment effects that satisfy fundamental principles drawn from the literature, and provide existence and welfare guarantees for endowment equilibria corresponding to endowment effects in this class. Our main results are the following: (1) For markets with XOS valuations, we introduce an endowment effect that is stronger than that of Babaioff et al. for which an endowment equilibrium is guaranteed to exist. Moreover, it gives at least half of the optimal welfare, and can be reached via a variant of the flexible ascent auction proposed by Fu et al. [EC'12]. (2) For markets with arbitrary valuations, we obtain a sweeping positive result by turning to markets in which it is allowed to bundle items into new indivisible items. In such settings, we show that there always exists an endowment equilibrium with optimal welfare. Moreover, we provide a polynomial algorithm that given an arbitrary allocation S, computes an endowment equilibrium with the same welfare guarantee as in S.
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